Being short for me (I'm 5'7) is a major thing. I really find it hard to get over. It's like women instantly disqualify you in their mind before you've even started talking, as if you don't even qualify as a man. And I don't even like tall girls, all the girls I approach or flirt with are 5'5 or shorter. It seems like tall guys get pretty girls and short guys get fatties. I know a guy my height who's about to marry a morbidly obese blob, he has no choice.

How do I get over this negative thinking? Everytime I chat girls up I feel like the annoying cocky short guy who's trying to compensate.

To the "You look young" part, don't be offended. Even if she(I'm guessing she is old, or looks older than you) says it in a negative tone, turn it and use it as a nag:

HB: You look so young / you are so young
You: Yeah, I know. It's great! Wish I never get old.

Implying that you are young, and she is getting old.